How so you simply solve a long equation with powers up to (5)? ( Please show steps)?

5x⁵ + 4x⁴ + 3x³ + 2x² - 70 = 0

Let f(x) = 5x⁵ + 4x⁴ + 3x³ + 2x² - 70 = 0

Put x = 2

f(2) = 5(2)⁵ + 4(2)⁴ + 3(2)³ + 2(2)² - 70 = 0

= 5 x 32 + 4 x 16 + 3 x 8 + 2 x 4 - 70

= 160 + 64 + 24 + 8 – 70

f(2) = 0

f(3) = 5(+3)⁵ + 4(3)⁴ + 3(3)³ + 2(3)² - 70

f(3) ≠ 0

f(-2) = 5(-2)⁵ + 4(-2)⁴ + 3(-2)³ + 2(-2)² - 70 = 0

= -160 + 64 - 24 + 8 - 70

f(-2) ≠ 0.

Not all fifth degree polynomial equations can be solved. One way you can go about attacking this problem is seeing if you can find the first root and use it to change it into a fourth degree equation. Then you can use the Method of Ferrari (https://www.encyclopediaofmath.org/index.php/Ferra... to solve that equation and to get the other four roots.

Alternatively, SOME fifth degree polynomials can be solved and you can read Wikipedia on "quintic equations" and http://mathworld.wolfram.com/QuinticEquation.html to see if you might have one of these.

If none of that works you can use numerical methods such as Newton's method.